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Publications Influence

Minimal identities of octonion algebras

- M. Racine
- Mathematics
- 15 May 1988

On montre que des octonions sur un corps de caracteristique non 2, 3 ou 5 ne satisfont pas d'identite polynomiale de degre 4 et que les identites de degre 5 sont toutes obtenues a partir de deux… Expand

22 6

Primitive Superalgebras with Superinvolution

- M. Racine
- Mathematics
- 15 August 1998

Abstract Our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras [ 5 , 6 , 10 ] and to classify primitive superrings with… Expand

47 5

Simple Jordan superalgebras with semisimple even part

- M. Racine, E. Zelmanov
- Mathematics
- 15 December 2003

55 4

On maximal subalgebras

- M. Racine
- Mathematics
- 15 June 1974

Let F be a field and &’ a unital (not necessarily associative) algebra over F. Our purpose is to determine the proper subalgebras of &’ which are maximal with respect to inclusion. This is done for… Expand

29 4- PDF

Springer forms and the first Tits construction of exceptional Jordan division algebras

- Holger P. Petersson, M. Racine
- Mathematics
- 1 October 1984

In this paper, a certain quadratic form, originally due to Springer [15], which may be associated with any separable cubic subfield living inside an exceptional simple Jordan algebra is related to… Expand

28 3

Jordan rings with nonzero socle

Let Jbe a nondegenerate Jordan algebra over a commutative associative ring $ containing j. Defining the socle @ of \ to be the sum of all minimal inner ideals of J, we prove that @ is the direct sum… Expand

32 3- PDF

Maximal subalgebras of central separable algebras

- M. Racine
- Mathematics
- 1978

Let A be a central separable algebra over a commutative ring R. A proper R-subalgebra of A is said to be maximal if it is maximal with respect to inclusion. THEOREM. Any proper subalgebra of A is… Expand

6 2- PDF

A simple proof of a theorem of Albert

- M. Racine
- Mathematics
- 1 February 1974

A simple proof is given of the following theorem of Albert: An associative division algebra of degree 4 over its center is of order 4 in the Brauer group if and only if it cannot be written as a… Expand

14 2

Minimal identities of symmetric matrices

Let Hn (F) denote the subspace of symmetric matrices of Mn (F), the full matrix algebra with coefficients in a field F . The subspace Hn (F) c Mn (F) does not have any polynomial identity of degree… Expand

18 2